Analytics and Modeling

This knowledge area embodies a variety of data driven analytics, geocomputational methods, simulation and model driven approaches designed to study complex spatial-temporal problems, develop insights into characteristics of geospatial data sets, create and test geospatial process models, and construct knowledge of the behavior of geographically-explicit and dynamic processes and their patterns.

Topics in this Knowledge Area are listed thematically below. Existing topics are linked directly to either their original (2006) or revised entries; forthcoming, future topics are italicized. 

 

Basic Spatial Operations Advanced Spatial Analysis Surface Analysis
Buffers Identifying & designing analytical procedures Calculating surface derivatives
Overlay Point pattern analysis Interpolation methods
Neighborhoods Cluster analysis Intervisibility
Map algebra Exploratory data analysis (EDA) Cost surfaces
  Analyzing multi-dimensional attributes  
Spatial Modeling Multi-criteria evaluation Network Analysis
Cartographic modeling Weighting schemes Least-cost (shortest) path analysis 
Components of models Spatial interaction Flow modeling
Coupling scientific models with GIS The spatial weights matrix The Classic Transportation Problem
Mathematical models Spatial interaction Other classic network problems
Spatial process models Space-scale algorithms Accessibility modeling
Using models to represent info & processes    
Workflow analysis and design Space-Time Analytics & Modeling Data Mining
  Computational movement analysis Data mining approaches
Data Manipulation Time geography Knowledge discovery
Approaches to point, line, area generalization   Pattern recognition
Coordinate transformations Spatial Statistics Geospatial data classification
Data conversion Global measures of spatial association Multi-layer feed-forward neural networks
Impacts of transformations Local measures of spatial association Rule learning
Raster resampling Spatial sampling for statistical analysis  
Vector-to-raster and raster-to-vector conversions Stochastic processes Spatial Simulation
  Outliers Simulation modeling
Analysis of Errors and Uncertainty  Bayesian methods Cellular automata modeling
Problems of currency, source, and scale Principles of semi-variogram construction Simulated annealing
Theory of error propagation Semi-variogram modeling Agent-based models
Propagation of error in geospatial modeling Kriging methods Adaptive agents
Fuzzy aggregation operators Principles of spatial econometrics Microsimulation & calibration of agent activities
  Spatial autoregressive models  
  Spatial filtering Spatial Optimization
  Kernels and density estimation Location-allocation modeling
  Spatial expansion & Geographically weighted regression Greedy heuristics
  Spatial distribution Interchange heuristics
  Mathematical models of uncertainty Genetic algorithms
  Non-linearity relationships and non-Gaussian distributions  
  Interchange with probability  

 

AM-41 - Flow modeling
  • Describe practical situations in which flow is conserved while splitting or joining at nodes of the network
  • Apply a maximum flow algorithm to calculate the largest flow from a source to a sink, using the edges of the network, subject to capacity constraints on the arcs and the conservation of flow
  • Explain how the concept of capacity represents an upper limit on the amount of flow through the network
  • Demonstrate how capacity is assigned to edges in a network using the appropriate data structure
AM-88 - Fuzzy aggregation operators
  • Compare and contrast Boolean and fuzzy logical operations
  • Compare and contrast several operators for fuzzy aggregation, including those for intersect and union
  • Exemplify one use of fuzzy aggregation operators
  • Describe how an approach to map overlay analysis might be different if region boundaries were fuzzy rather than crisp
  • Describe fuzzy aggregation operators
AM-78 - Genetic algorithms and artificial genomes
  • Create an artificial genome that can be used in a genetic algorithm to solve a specific problem
  • Describe a cluster in a way that could be represented in a genome
  • Explain how and why the representation of a GA’s chromosome strings can enhance or hinder the effectiveness of the GA
  • Use one of the many freely available GA packages to apply a GA to implement a simple genetic algorithm to a simple problem, such as optimizing the location of one or more facilities or optimizing the selection of habitat for a nature preserve geospatial pattern optimization (such as for finding clusters of disease points)
  • Describe a potential solution for a problem in a way that could be represented in a chromosome and evaluated according to some measure of fitness (such as the total distance everyone travels to the facility or the diversity of plants and animals that would be protected) genome
AM-77 - Genetic algorithms and global solutions
  • Describe the difficulty of finding globally optimal solutions for problems with many local optima
  • Explain how evolutionary algorithms may be used to search for solutions
  • Explain the important advantage that GA methods may offer to find diverse near-optimal solutions
  • Explain how a GA searches for solutions by using selection proportional to fitness, crossover, and (very low levels of) mutation to fitness criteria and crossover mutation to search for a globally optimal solution to a problem
  • Compare and contrast the effectiveness of multiple search criteria for finding the optimal solution with a simple greedy hill climbing approach
AM-65 - Geospatial data classification
  • Compare and contrast the assumptions and performance of parametric and non-parametric approaches to multivariate data classification
  • Describe three algorithms that are commonly used to conduct geospatial data classification
  • Explain the effect of including geospatial contiguity as an explicit neighborhood classification criterion
  • Compare and contrast the results of the neural approach to those obtained using more traditional Gaussian maximum likelihood classification (available in most remote sensing systems)
AM-22 - Global measures of spatial association
  • Describe the effect of the assumption of stationarity on global measures of spatial association
  • Justify, compute, and test the significance of the join count statistic for a pattern of objects
  • Compute the K function
  • Explain how a statistic that is based on combining all the spatial data and returning a single summary value or two can be useful in understanding broad spatial trends
  • Compute measures of overall dispersion and clustering of point datasets using nearest neighbor distance statistics
  • Compute Moran’s I and Geary’s c for patterns of attribute data measured on interval/ratio scales
  • Explain how the K function provides a scale-dependent measure of dispersion
AM-73 - Greedy heuristics
  • Demonstrate how to implement a greedy heuristic process
  • Identify problems for which the greedy heuristic also produces the optimal solution (e.g., Kruskal’s algorithm for minimum spanning tree, the fractional Knapsack problem)
AM-53 - Identifying and designing analytical procedures
  • Identify the sequence of operations and statistical/mathematical methods (a procedure) appropriate for a particular application (e.g., multi-criteria evaluation for site suitability)
  • Implement a pre-defined procedure for a sample dataset
  • Develop a planned analytical procedure to solve a new unstructured problem (e.g., long-term business strategy)
  • Critique the necessity of the operations used in a pre-defined procedure for a particular application (e.g., suitability analysis)
AM-56 - Impacts of transformations
  • Compare and contrast the impacts of different conversion approaches, including the effect on spatial components
  • Create a flowchart showing the sequence of transformations on a data set (e.g., geometric and radiometric correction and mosaicking of remotely sensed data)
  • Prioritize a set of algorithms designed to perform transformations based on the need to maintain data integrity (e.g., converting a digital elevation model into a TIN)
AM-74 - Interchange heuristics
  • Define alternatives to the Tietz and Bart heuristic
  • Outline the Tietz and Bart interchange heuristic
  • Describe the process whereby an element within a random solution is exchanged, and if it improves the solution, it is accepted, and if not, it is rejected and another element is tried until no improvement occurs in the objective function value

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